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The purpose of this paper is to describe an adaptive algorithm for improving the performance of Bayesian Network Classifiers (BNCs) in an on-line learning framework. Instead of choosing a priori a particular model class of BNCs, our adaptive algorithm scales up the model's complexity by gradually increasing the number of allowable dependencies among features. Starting with the simple Naïve Bayes structure, it uses simple decision rules based on qualitative information about the performance's dynamics to decide when it makes sense to do the next move in the spectrum of feature dependencies and to start searching for a more complex classifier. Results in conducted experiments using the class of Dependence Bayesian Classifiers on three large datasets show that our algorithm is able to select a model with the appropriate complexity for the current amount of training data, thus balancing the computational cost of updating a model with the benefits of increasing in accuracy.